id stringlengths 27 136 | text stringlengths 4 1.05M |
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18216 | +0
# help
0
70
2
Simplify √(8 - 4√3)
Jul 27, 2021
#1
+181
+1
Factor out $2^2$ from each of the numbers to get...
$\boxed{2\sqrt{2-\sqrt{3}}}$
Jul 27, 2021
#2
+2193
+1
Nice, but I think that it can be simplified further.
sqrt(a) - sqrt(b) = sqrt(8-4sqrt(3))
a + b - 2sqrt(ab) = 8 - 4sqrt(3)
a + b = 8
ab = 12... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18217 | Lemma 33.14.1. Let $X$ be a scheme which is locally of finite type over $k$. Then
1. for any closed point $x \in X$ the extension $\kappa (x)/k$ is algebraic, and
2. $X$ is a Jacobson scheme (Properties, Definition 28.6.1).
Proof. A scheme is Jacobson if and only if it has an affine open covering by Jacobson schemes... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18218 | The Yablo Paradox implies there is no way to coherently assign a truth value to any of the sentences in the countably infinite sequence of sentences, each of the form, “All of the subsequent sentences are false.” Specifically, the Yablo Paradox arises when we consider the following infinite sequence of sentences:
\beg... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18219 | # zbMATH — the first resource for mathematics
A hybrid method for monotone variational inequalities involving pseudocontractions. (English) Zbl 1215.49021
Summary: We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point $$x^*$$ with the property $$x^*\in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18220 | # Indefinite integral with discontinuous integrand
1. Jun 29, 2015
Suppose $f$ is defined as follows:
$f(x) = 1$ for all $x ≠ 1$, $f(1) = 10$.
Is the indefinite integral (or the most general antiderivative) of $f$ defined at $x = 1$?
I'm asking this question because I already know how to deal with, say, $\int_0^2 f$;... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18221 | # What is the vertex form of y= 2x^2-16x+32 ?
Mar 2, 2018
$y = 2 {\left(x - 4\right)}^{2}$
#### Explanation:
To find the vertex form, you need to complete the square. So set the equation equal to zero, then separate the coefficient of x, which is 2:
$0 = {x}^{2} - 8 x + 16$
Move the ones (16) to the other side, the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18222 | Home
>
English
>
Class 8
>
Maths
>
Chapter
>
Data Handling
>
Let m be the mid - point and l...
# Let m be the mid - point and l the upper class limit of a class in a continuous frequency distribution The lowe limit of the class is
Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!
2m+l2m-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18223 | # Confusing log limit
## Homework Statement
$$\lim\limits_{x \to 0} \left(\ln(1+x)\right)^x$$
## Homework Equations
Maclaurin series:
$$\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} + ... + (-1)^{r+1} \frac{x^r}{r} + ...$$
## The Attempt at a Solution
We're considering vanishingly small $x$, so just taking the fir... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9808 | # Convert a Complex Number to Polar and Exponential Forms - Calculator
An easy to use calculator that converts a complex number to polar and exponential forms. The idea is to find the modulus r and the argument θ of the complex number such that
z = a + i b = r ( cos(θ) + i sin(θ) ) , Polar form
z = a + ib = r e , Ex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9809 | ## FANDOM
10,821 Pages
I really should have made this blog post sooner than after two years, but oh well, at least I am making it now. In what follows I will refer to my old blog post.
TL;DR: When I have defined FOOT (and BIG FOOT) I have a somewhat bottom-up language to describe it, starting from the universe of se... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9810 | # Fundamental theorem of algebra and factoring?
1. Jul 23, 2015
### pellman
Is the fundamental theorem of algebra (for polynomials on the complex plane) equivalent to the statement that any polynomial p of degree n>0 can be written
$$p(z) = c(z - a_1 ) (z- a_2) \cdot \cdot \cdot (z - a_n )$$
or am I missing some s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9811 | ## Not signed in
Want to take part in these discussions? Sign in if you have an account, or apply for one below
## Discussion Tag Cloud
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 12th 2018
• (edited 6 days ago)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9812 | +0
# Putnam Competition Clarification
0
36
2
$$\int_0^{1}\frac{\ln(x+1)}{x^2+1}dx$$
Guest Jun 5, 2018
#1
+793
+2
Hey Guest,
I have slept on it, and finished the solution.
First, we use $$x = \tan θ$$
We can rewrite the desired integral as $$\int_0^{\pi/4}\log(\tan(\theta)+1)d\theta$$
Also:
$$\log(\tan(θ) + 1)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9813 | ## Possible bug in some probability commands
Following an example from the documentation
``````Expectation[x^2 + 3 y^2 + 11, {x, y} [Distributed] DirichletDistribution[{1, 4, 5}]]
``````
`636/55`
, I try
``````Expectation[x^2 + y^2, {x, y} [Distributed] UniformDistribution[{-1, 2}]]
``````
, but obtain the return... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9814 | 1. Math
2. Calculus
3. calculate the arc length for xt34t yt23t from 2 to...
# Question: calculate the arc length for xt34t yt23t from 2 to...
###### Question details
calculate the arc length for:
x=t3-4t y=t2-3t
from -2 to 2
I'm able to simplify it down to but I'm not sure where to go from here. I can plug it... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9815 | Derivation of parametric function
1. Jan 18, 2007
kasse
I get the first derivative correct, but what's wrong with my attempt to find the second derivative?
2. Jan 18, 2007
Schrodinger's Dog
a) the bottom line is wrong
should be $$\frac {cos(t)-1}{(1-cos(t))^2}$$
and b) you need to further simplify to get the an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9816 | # Is every parallelogram a rectangle ??
Let's say we have a parallelogram $\text{ABCD}$.
$\triangle \text{ADC}$ and $\triangle \text{BCD}$ are on the same base and between two parallel lines $\text{AB}$ and $\text{CD}$, So, $$ar\triangle \text{ADC}=ar\triangle \text{BCD}$$ Now the things those should be noticed are t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9817 | # nLab Wick's lemma
Contents
### Context
#### Measure and probability theory
measure theory
probability theory
# Contents
## Idea
Wick’s lemma is a combinatorial formula for the product in associative algebras that appear in the context of free field theory.
From the point of view of path integral quantization... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9818 | # If Ey (X + 1) = 1, Show That (D^2y)/(Dx^2) =((Dy)/(Dx))^2 - Mathematics
If ey (x + 1) = 1, show that (d^2y)/(dx^2) =((dy)/(dx))^2
#### Solution 2
Is there an error in this question or solution?
#### APPEARS IN
NCERT Class 12 Maths
Chapter 5 Continuity and Differentiability
Q 16 | Page 184 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9819 | # Relation with each projection finite or cofinite
Suppose $S$ is a k-ary relation on $\mathbb{N}$. Given $1 \leq i \leq k$, define $\pi_i(S)$ in the following way: $$\left \{s_i | (s_1, s_2, \cdots s_i \cdots s_k) \in S \right \}$$.
We call $S$ nice if: for every component $i$, either the projection $\pi_i(S)$ or it... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9820 | # $\text{Original \& Alternating}$
\begin{aligned} 1 + \dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 + \dfrac16 + \dfrac17 + \dfrac18 + \dots &= \infty \\ 1 - \dfrac12 + \dfrac13 - \dfrac14 + \dfrac15 - \dfrac16 + \dfrac17 - \dfrac18 + \dots &= \ln2 \\ \\ 1 + \dfrac13 + \dfrac15 + \dfrac17 + \dfrac19 + \dfrac{1}{11} + \df... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9821 | ## Same functions over the set of rational numbers
For college and university level advanced Mathematics
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am
### Same functions over the set of rational numbers
If two functions, both defined from R to R, take same values for each rational argument, they are equal. Ne... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9822 | # What is 7 over the square root of 27?
Jul 24, 2015
$\frac{7 \sqrt{3}}{9}$
#### Explanation:
Start by writing your expression, which features $7$ in the numerator and $\sqrt{27}$ in the denominator.
7/(sqrt(27)
Now, the important thing to realize here is that you can write $27$ as
27 = 9 * 3 = 3 * 3 * 3 = 3""^2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9823 | # What is the 'true' value of a probability parameter?
We seem to distinguish empirical estimates of parameters from 'true' values, and make comparisons between the two. I can understand what an empirical estimate is. What is a 'true' value?
For instance, my course notes have:
Definition 4.7 (Consistent estimator) A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9440 | Be careful with this series!
Geometry Level 5
$\sum_{r=1}^{\infty}\cot^{-1} \left (\dfrac{r^2}{8} \right) = \dfrac{m}{n} \pi$
If the equation above holds true for mutually prime positive integers $$m$$ and $$n$$, find $$m+n$$.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9441 | Home » » Find the number of ways of selecting 6 out of 10 subjects for an examination
# Find the number of ways of selecting 6 out of 10 subjects for an examination
### Question
Find the number of ways of selecting 6 out of 10 subjects for an examination
### Options
A) 128
B) 216
C) 215
D) 210
$$^{10}C_6 = \fr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9442 | # A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
I would like to prove the statement in the title.
Proof: We prove that if $f$ is not strictly decreasing, then it must be strictly increasing. So suppose $x < y$.
And that's pretty much how far I g... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9443 | # Factorising F-tensors by diagrammatic tensor notation
#### by Stephen McAteer
Institution: Department of Mathematics and Statistics, The University of Melbourne
Date: Tue 8th March 2011
Time: 1:00 PM
Location: Room 215, Richard Berry Building, The University of Melbourne
Abstract: In 1996 Maillet and Sanchez de Sa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9444 | # Binomial Expansion alternating Sum
1. Aug 19, 2011
### Punkyc7
use the binomial expansion formula to find the alternating sum of the numbers in row n of Pascals triangle.
nC0-nC1+nC2.....
So I wrote a few rows of the triangle and it looks like once you get past row zero the alternating sum of the numbers in the r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9445 | # Current Affairs 6th Class
#### Algebra
Algebra
• Algebra is a branch of mathematics in which Arithmetic is generalised.
• We use lower case English alphabets called literals to represent quantities instead of particular numbers. Literals are also used for representing unknown quantities.
• Literals take different... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9446 | ## Adjoint of Inner Product Example
Let
$V$
be the vector space of polynomials over the field of complex numbers with inner product
$f \cdot g= \int^1_0 f(t) \bar{g} (t) dt$
(where
$\bar{g} (t)$
) is the complex conjugate of
$g(t)$
.
What is the adjoint of the linear operator
$M_f(g)=fg$
(multiplication by
$f$
?)
If... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9447 | Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition
Here P = 0.69 a. $P(none Play) = (1 - 0.69)^{4} = 0.009$ b. $P (All Play) = (0.69)^{4} = 0.227$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9448 | # Sequence Fractals Part I #1
$z^2+c+s_i$
si = 1, -1, 1, -1, …
Center: -1.8+0i, Zoom = 0.4.
The description “combine fractal and sequence” is intentionally vague. Part I will look at the simplest way to combine fractals and sequences, namely “just add”. The sequence in this case is simple, alternating 1 and -1.
Defi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9449 | # Thread: Economics - import elasticity question
1. ## Economics - import elasticity question
Hi, I'm trying to follow the working from a paper* that looks at the revenue maximising tariff for a country.
It gives the expression for a government's tariff revenue as:
R = t.p.M
where R is revenue, t is the average ad v... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9450 | Law of sine and cosine problem
• May 8th 2010, 02:28 PM
jwu
Law of sine and cosine problem
Just a simple problem. But I got stuck on some points.
We just learned the law of sine and the law of cosine from class.
And here's the assignment according this two topics:
Solve each triangle. Give lengths to three significan... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9451 | # Renormalization in Two Dimensions
Gold Member
## Homework Statement
I am looking for references for the scalar field theory in one-space, one-time dimension defined by:
$$\mathcal{L}=-\frac{1}{2}(\partial_{\mu}\phi)^2-\frac{1}{2}m_{2,0}^2\phi^2-\frac{1}{4!}m_{4,0}^2\phi^4-\frac{1}{6!}m_{6,0}^2\phi^6$$
That expla... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9452 | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
A couple by Serre. Homologie singulière des éspaces fibrés has as clear and economical an account of spectral sequences as I've seen anywhere. The method of Groupes d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9453 | # Micro-level water-resources engineering—6: Evaporation
As compared to the last year, public awareness about water resources has certainly increased this year. It has been a second drought-year straight in a row. None can miss it—the water issue—now. [Not even the breweries.]
There are several NGO initiatives involv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9454 | # What is the angular momentum of a rod with a mass of 15 kg and length of 7 m that is spinning around its center at 19 Hz?
Jan 16, 2018
The angular momentum is $= 7312.1 k g {m}^{2} {s}^{-} 1$
#### Explanation:
$\text{Angular momentium" (kgm^2s^-1)="Moment of inertia"(kgm^2)xx"Angular velocity } \left(r a {\mathrm... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_9455 | Strong Induction for a sequence inequality?
On the previous midterm, there was a question that I couldn't solve. It gave us this sequence
The sequence $$a_0, a_1, a_2,...$$is defined by $$a_0 = 1,$$ and for all integers $$n > 0,$$ $$a_n = a_{\lfloor n/2 \rfloor} + a_{\lfloor 2n/3 \rfloor} + n.$$
Prove by Strong Indu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2032 | # Standard noI? Tanddrn vanadie and calculate the folowing probabilities _ arawing Dictures Aneredem appropnate (Round Your answers (our decimal places;)USE
standard noI? Tanddrn vanadie and calculate the folowing probabilities _ arawing Dictures Aneredem appropnate (Round Your answers (our decimal places;) USE SALT (... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2033 | ## RRB NTPC Quant Test 49
Instructions
For the following questions answer them individually
Q 1
An object travels 24 m in 3 s and then another 15 m in 2 s. What is the average speed of the object?
Q 2
I walk a certain distance and ride back, taking $$\frac{13}{2}$$ hours in total. I could walk both ways in a tota... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2034 | # Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 32
$-4-5i$
#### Work Step by Step
Removing the grouping symbols and then adding the real parts and the imaginary parts, the given expression, $(5-3i)-(9+2i) ,$ simplifies to \begin{array}{l}\require{cancel} 5-3i-9-2i \\\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2035 | 1. ## Word problem help please!
11 years ago Helen was four times as old as Ed. In one year Helen will be two times Ed's age. How old are they now?
I also need to see the formula so I can try to learn the process. Thanks
so much!
2. 17 and 35?
3. ## word problem help please!
I also need to know how to do it! Thank... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2036 | # Newtons cradle, conservation of momentum
1. May 21, 2014
### Bengo
1. The problem statement, all variables and given/known data
I don't understand how momentum is conserved in Newtons cradle. If I look at the component vectors for the initial ball on the left that I raise, one component points down and one points ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2037 | # Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm{dx}$
Evaluate $$\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm{dx}$$
-
Isn't it an improper one? +1. – B. S. Jan 18 '13 at 14:09
BabaSorouh: an improper integral is also a definite integral that has an integrand that approache... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2038 | # nLab singular knot
### Context
#### Topology
topology
algebraic topology
## Idea
A singular knot is a smooth map (or isotopy class of smooth maps) $S^1 \to \mathbb{R}^3$ which is not an embedding. That is, it is not a knot. Singular knots come in various flavours according to the ways in which it is possible to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2039 | # how to get chi square distribution to N(0,1) [closed]
Let $$X_1,X_2,...,X_n$$ be a random sample from chi square distribution. Let $$x̄$$ be the sample mean. How would you use the central limit theorem to get this approximation:
$$\frac{\left(x̄-1\right)}{\sqrt{\frac{2}{n}}}$$ ~ $$Normal(0,1)$$
also how would one ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2040 | # Homework Help: Triple Integral
1. Sep 15, 2011
### triden
1. The problem statement, all variables and given/known data
Evaluate $\underbrace{\int\int\int}_{Q}(1-x) dzdydx$
Where Q is the solid that lies in the first octant and below the plane:
3x + 2y + z = 6
3. The attempt at a solution
I guess my main proble... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2041 | Inflation in the Mixed Higgs-R^{2} Model
# Inflation in the Mixed Higgs-R2 Model
## Abstract
We analyze a two-field inflationary model consisting of the Ricci scalar squared () term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein term. Detailed analysis of the power spectrum... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2042 | # Main Page
#### Fractals | Dynamics | Combinatorics | Hyperoperators | History | Help
Tetration by Escape Tetration by Period
My name is Daniel Geisler, welcome to my web site dedicated to promoting research into the question of what lies beyond exponentiation. Tetration is defined as iterated exponentiation b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2043 | ## Algebra: A Combined Approach (4th Edition)
Published by Pearson
# Appendix A - Exercise Set - Page 975: 23
#### Answer
$(9y^2 - 7y + 5) - (8y^2 - 7y + 2)$ $= y^2 + 3$
#### Work Step by Step
$(9y^2 - 7y + 5) - (8y^2 - 7y + 2)$ $= 9y^2 - 8y^2 - 7y + 7y + 5 - 2$ (Change signs and group like terms) $= y^2 + 3$ (Co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2044 | 7th Edition 6N.3c
$E_{cell} = E_{cell}^{\circ}-\frac{RT}{nF}\ln Q$
Samantha Ito 2E
Posts: 64
Joined: Fri Sep 28, 2018 12:29 am
7th Edition 6N.3c
For Q in the solutions manual, the partial pressures are in the numerator and the concentrations are in the denominator. Are you allowed to mix partial pressures and conce... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2045 | Question
n identical cells, each of emf E and internal resistance r, are joined in series to form a closed circuit.
The potential difference across any one cell is:
(a) E
(b) E/n
(c) (n-1)/n E
(d) Zero
Solution
Current in circuit, i = (nE)/(nr)= E/r
The equivalent circuit of one is shown in figure.
Potential ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2046 | Twenty coins and no balance
On the table there are $20$ coins that carry the letters $A,B,C,\ldots,T$. The values of these coins are $1,2,3,\ldots,20$ Euro (but the assignment of values to letters is secret). Fredo knows the value of every single coin, while Cosmo does not know.
In every round of the game, Cosmo must... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2047 | SERVING THE QUANTITATIVE FINANCE COMMUNITY
CactusMan
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QuoteOriginally posted by: CactusManWho here is into this and can talk ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2448 | # Choosing a Cauchy sequence for a real
It is easy to form in ZF, for each real $$a$$, a "canonical" Cauchy sequence that converges to $$a$$. For example, one can take the sequence of finite initial segments of the decimal expansion of $$a$$, being careful when $$a$$ is a base-10 rational to pick one of the two decima... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2449 | group theory
# Contents
## Definition
### For abelian groups
###### Definition
For $A$, $B$ and $C$ abelian groups and $A×B$ the cartesian product group, a bilinear map
$f:A×B\to C$f : A \times B \to C
from $A$ and $B$ to $C$ is a function of the underlying sets (that is, a binary function from $A$ and $B$ to $C... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2450 | # Use Excel to solve problem three. If you are submitting a hard copy of your exam,...
#### Similar Solved Questions
##### Solve the given problems. The periodic force $F$ (in $\mathrm{N}$ ) applied in testing a spring system can be represented by $F=0$ for $-\pi \leq t<0$ and $F=t^{2}+t$ for $0<t<\pi,$ where the tim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2451 | # A Karrass-Solitar theorem for surface groups
Let $\Gamma_g$ be a surface group of genus $g \geq 2$. That is, there is a presentation $$\Gamma_g = \langle x_1, y_1, \dots, x_g, y_g \vert \prod_{i = 1}^{g}[x_i,y_i] = 1\rangle$$
Is there a nontrivial, finitely generated $N \lhd \Gamma_g$ of infinite index?
More gener... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2452 | # Tag Info
12
Let me show how to roll your own numerical solution to a non-linear integral equation using a collocation method. It's fun! This will involve two approximations. First, we will approximate the function B[x] by its values at n particular points in the range {x, 0, 1}. The integral over x will be replaced... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2453 | ### Sample Papers
Download the PDF Sample Papers Free for off line practice and view the Solutions online.
### Book Store
Download books and chapters from book store.
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### Test Series
Pre-Board Question Papers are now available online for students to practice and excel the exams b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2454 | #### Explanation:
We first notice that 20%=20/100=1/5. So, the discount will be $\frac{1}{5}$ of the marked price. Therefore, we multiply the marked price by $\frac{1}{5}$ to get the discount.
$35*1/5=$7 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2455 | ## Example Problems on Sequences of Random Variables
ST779 Homework 6 on Sequences of Random Variables
# 1
Let $X_{1}, X_{2}, \dots$, be i.i.d. with $P(X_{1} = 1) = p = 1 - P(X_{1}=-1)$ and $S_{n} \sum_{i=1}^{n} X_{i}$.
Is $\{ S_n = 0 \text{ infinitely often} \}$ a tail event? Supply arguments.
Show that if $p \ne... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2456 | # zbMATH — the first resource for mathematics
## Communications of the Korean Mathematical Society
Short Title: Commun. Korean Math. Soc. Publisher: Korean Mathematical Society, Seoul ISSN: 1225-1763; 2234-3024/e Online: http://www.koreascience.or.kr/journal/DBSHCJ.pagehttp://ckms.kms.or.kr/ Comments: Indexed cover-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2457 | # Pandoc 转成 Word
Pandoc 是个通用的文件转换工具，支持扩展的 Markdown 以及 $$\LaTeX$$ 语法，也就是说基本可以满足你的写作和写论文需求，还支持代码高亮，所以你还可以用来写程序文档。
# Euclidean distance in various coordinate systems
The distance formula in Cartesian coordinates is derived from the Pythagorean theorem.[^37] If $(x1, y1)$ and $(x2, y2)$ are points in the plane, then the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2458 | # Second derivative
$F'(x) = \frac{d}{dx} \int_1^x f(t) dt = f(x)$ by the fundamental theorem of calculus. So $F''(2) = f'(2)$.
You can find $f'(t)$ using the fundamental theorem of calculus as well. You should get $f'(t) = 4t^3 \frac{\sqrt{5+t^{16}}}{t^4}$ (there's a chain rule application in there as well). |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2459 | ## Monday Math 50
Let us consider Laplace’s equation, in two dimensions. In Cartesian coordinates, this is . We can see by immediate inspection that linear functions f(x,y)=ax+by+c satisfy this. We also see that terms of the form axy satisfy the equation.
A useful method for finding general solutions is the separati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2460 | # minimizing sum of distances
I've been working on a problem recently, and I was hoping you all could help me out. The issue is basically this:
Consider a set of $n$ points $x_1$, $x_2 \ldots x_n$ in a plane $P$. You want to find a point $x_i$ such that the sum of distances between $x_i$ and every other point is mini... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2461 | Bipartite Graph to solve the wolf river crossing problem
I have just started studying about bipartite graphs and there is an example that bipartite graph can be use to solve the wolf, cabbage, and the sheep river crossing problem, as a kid i had fun solving this question, now I was wondering how can we describe the pr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2462 | ### Primary 4 Problem Sums/Word Problems - Try FREE
Score :
Disabled
#### Question 1 of 4
A dress boutique has a total of 848 shirts and trousers.
3/7 of the shirts is equal to 1/3 of the trousers.
(a) How many shirts are there in the boutique?
(b) How many trousers are there in the boutique?
Notes to students:
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_2463 | # Find the value of \tan(\frac{\pi}{3})
Find the value of $$\displaystyle{\tan{{\left({\frac{{\pi}}{{{3}}}}\right)}}}$$
• Questions are typically answered in as fast as 30 minutes
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Well, $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7200 | If Z is an integer, is Z prime? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
It is currently 22 Feb 2017, 14:22
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7201 | MTH435
Introduction to Mathematical Analysis I
MW 3:00-4:15 PM
Lippitt Hall 205
Instructor Araceli Bonifant
Office: Lippitt Hall 200 B
Phone: 874-4394
Email: bonifant@math.uri.edu
Office Hours: Tuesday 2:00PM, Wednesday 2:00PM
Book: Introduction to Real Analysis, 3rd Edition by Robert G. Bartle and Donald R. She... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7202 | # 2. Derivatives of Csc, Sec and Cot Functions
by M. Bourne
By using the quotient rule and trigonometric identities, we can obtain the following derivatives:
(d(csc x))/(dx)=-csc x cot x
(d(sec x))/(dx)=sec x tan x
(d(cot x))/(dx)=-csc^2 x
In words, we would say:
The derivative of csc x is -csc x cot x,
The deri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7203 | Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
How many different ways can you choose 3 vowels out of the box, if there are 5 vowels in the box and order does not matter?
10 different ways
There are 5 vowels and we need to take 3 and order d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7204 | H. XOR and Distance
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
You are given an array $a$ consisting of $n$ distinct elements and an integer $k$. Each element in the array is a non-negative integer not exceeding $2^k-1$.
Let's define the XOR distance ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7205 | # $D$-modules and quasi-projective varieties?
Until recently I was under the impression, that for any morphism $f:X\rightarrow Y$ of smooth complex varieties there exist functors six functors $f^*,f_{*},...$ between the derived categories of $\cal D$-modules with bounded holonomic cohomology.
However the experts assu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7206 | # Finite-sample Guarantees for Winsorized Importance Sampling
Importance sampling is a widely used technique to estimate the properties of a distribution. The resulting estimator is always unbiased, but may sometimes incur huge variance. This paper investigates trading-off some bias for variance by winsorizing the imp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7207 | You are currently browsing the tag archive for the ‘group cohomology’ tag.
Let ${G = (G,+)}$, ${H = (H,+)}$ be additive groups (i.e., groups with an abelian addition group law). A map ${f: G \rightarrow H}$ is a homomorphism if one has
$\displaystyle f(x+y) - f(x) - f(y) = 0$
for all ${x,y \in G}$. A map ${f: G \rig... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7208 | # Question #9db85
May 20, 2017
$9 \cdot {10}^{5} \text{g}$
#### Explanation:
In order to be able to answer this question, you must know the enthalpy of fusion of water
$\Delta {H}_{\text{fus" = "333.55 J g}}^{- 1}$
The enthalpy of fusion tells you the amount of energy needed in order to convert $\text{1 g}$ of a ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7209 | # A Non-recursive Fibonacci Sequence
How can I determine the general term of a Fibonacci Sequence? Is it possible for any one to calculate F2013 and large numbers like this?
Is there a general formula for the nth term of the Fibonacci Sequence?
If there is a combinatorial formula, that is more preferable; some formul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7210 | # Bashing Telescope
Algebra Level 5
$\large\sum_{n=1}^{24}\frac{7n^{3}+41n^{2}+88n+72}{n^{5}+10n^{4}+35n^{3}+50n^{2}+24n}$ If the value of the above expression is in the form of $$\dfrac{A}{B}$$, where $$A,B$$ are positive coprime integers then find the value of $$A+B$$.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7211 | 16 views
I have a doubt, How many rows will be returned when All values of R2.A will be Null….in this case number of rows Natural Join should give 0 rows ….what will be minimum number of rows???
ago | 16 views
I think you’re correct. In fact it R2.A need not even be NULL, any non NULL values such that $R_2.A \cap R_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7212 | # Polynomial division problem
Let $f(x) = x^{10}+5x^9-8x^8+7x^7-x^6-12x^5+4x^4-8x^3+12x^2-5x-5.$
Without using long division (which would be horribly nasty!), find the remainder when $f(x)$ is divided by $x^2-1$.
I'm not sure how to do this, as the only way I know of dividing polynomials other than long division is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7213 | # Why is the set of integers in $\mathbb{R}$ closed?
A point $p$ is a limit point of the set $E$ if every neighbourhood of $p$ contains a point $q \not= p$ such that $q \in E$
So there are no limit points in $\mathbb{Z} \in \mathbb{R}$
Is that why it's closed?
A point $p$ is an interior point of the set $E$ if ther... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7214 | # Matrix element squared for up + antidown -> photon + W boson? [closed]
I am in trouble… I am a master student (first year) in theoretical particle physics and I have been working for several months on the calculation of the total cross-section at leading order for the process:
$$u + \overline{d} \rightarrow W^{+} +... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7215 | # How do you solve the system using the elimination method for 2x+3y=19 , 8x-3y=-14?
Jul 7, 2015
$\left(x , y\right) = \left(\frac{1}{2} , 6\right)$
#### Explanation:
[1]$\textcolor{w h i t e}{\text{XXXX}}$$2 x + 3 y = 19$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$8 x - 3 y = - 14$
Add [1] and [2] (eliminating the $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18272 | ## Ralfativity vs Relativity: the final summation
This is not an everything goes forum, but rather a place to ask questions and request help for developing your ideas.
### Re: Ralfativity vs Relativity: the final summation
Ralf, this happens to everyone that tries to develop their own theory or interpretation of rel... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18273 | # Tag Info
## New answers tagged vectors
0
When we decompose vector into it's rectangular components, we get two vectors along x-axis and y-axis. So the vector in the second diagram may have its x-component as a vector also whose magnitude is $F\cos\theta$ and direction is same as $\vec{S}$ i.e. along positive x-axi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18274 | Competitions
# Two identical digits
Four-digit number is given. Determine whether it contains exactly two different digits, each of these digits must occur twice. For example, the numbers 2727 and 6677 satisfy this condition.
#### Input
One four-digit number.
#### Output
Print "YES" if the number satisfies the sp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18275 | # Homework Help: Vectors and planes
1. Jan 24, 2006
### Shay10825
Hello. I need some help with the following problem:
Find the component of u if u is perpendicular to the plane x- 3y + 4z =0 and the magnitude of u is 3.
My work:
Some vector v is on the plane
v = 1i – 3j + 4k
so then the dot product of u and v =... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18276 | Mathematics » Polynomials II » Special Products
# Special Products Summary
## Key Concepts
• Binomial Squares Pattern
• If $$a,b$$ are real numbers,
• $${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$$
• $${\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}$$
• To square a binomial: square the first term, square the last term, d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18277 | ## Section16.13The Law of Sines and The Law of Cosines
##### The Law of Sines.
The law of sines is a proportionality law relating the various parts of a triangle. The law is stated below. The variables reference the parts of the triangle shown in Figure 16.13.1. Note that angle $\alpha$ is opposite side $a\text{,}$ a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18278 | # How to interpret the standard deviation of a discrete random variable
How would you interpret the standard deviation of a discrete random variable and state it simply for someone with limited statistical background? For example,
Assume I am betting on an event with a 21% chance of occurring. If I bet it will occur ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18279 | A propped cantilever of span $L$ carries a vertical concentrated load at the mid-span. If the plastic moment capacity of the section is $M_p$, the magnitude of the collapse load is
1. $\dfrac{8M_p}{L} \\$
2. $\dfrac{6M_p}{L} \\$
3. $\dfrac{4M_p}{L} \\$
4. $\dfrac{2M_p}{L}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18280 | ACTA issues
## Computation of the $\rho$-numerical radius for truncated shifts
Laurent Carrot
Acta Sci. Math. (Szeged) 69:1-2(2003), 311-322
2897/2009
Abstract. We are interested in computing the $\rho$-numerical radius of the truncated shift $S_n$ on $l_2^n$. This value, first computed for $\rho =2$ by Haagerup a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18281 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Distances or Dimensions Given Scale Measurements
## Identify actual dimensions given scale dimensions
Estimated7 minsto complete
%
Progress
Practice Distances or Dimensions Given Scal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18282 | # How do you evaluate e^( ( pi)/2 i) - e^( ( 2 pi)/3 i) using trigonometric functions?
Jan 10, 2017
The value of this expression is $\frac{1}{2} + \left(1 - \frac{\sqrt{3}}{2}\right) i$
#### Explanation:
To evaluate this expression you have to write the complex numbers in algebraic form. To do this you use the ide... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18283 | # Difficulties in computing the derivatives of the Dirichlet distribution
I need to compute the first derivatives of the Dirichlet distribution, defined in the following way:
$$r(P; \pi, \rho) = \frac{\Gamma(c)}{\prod_{i=1}^{k} \Gamma(c \pi_i)} \cdot \prod_{i=1}^{k} P_i^{c\pi_i - 1},$$
where $$c=\rho^{-2}(1-\rho^2) ... |
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